amount, dozen

The usual rule for "amount vs number" is that "number" is used with plural nouns that are countable while "amount" is used with singular, mass, uncountable nouns. a problem arises with "people" because, depending on how you view the situation, "people" can be plural or singular and they may or may not be a mass, uncountable group. So in both of your sentences you could use "number" or "amount" depending on the specifics of the situation. In the second sentence "A great amount of people" would be better if you go with "amount." I'm not sure of the rule on that.

As far as "dozen" goes, it is twelve of anything, objects or people.   Something I only just realized I don't know is a rule of when to put an "s" after dozen.   In your first sentence, "a few dozen" would sound better but I don't know the rule. If you had said, "dozens are still pushing in" you could have added the "s" but I don't know why.   Maybe someone else can tell us.

I affirm what Dick wisely says: It should be a few dozen in this case and usually -- unless the people are physically grouped in twelves. A few dozen represents a gross quantity. A few dozens represents a count of individual sets of twelve. (e.g. He stood at the curb with a bucket of 20 dozens of roses.) The same holds for gross, score, hundred, thousand, million, myriad, etc.

Wikipedia has a decent summary here under the rubric Plurals of numbers English Plurals.

Dick is also right about amount vs. number, but I find the use of amount of people less jarring than a few dozens. Number of people is better.

Half a dozen soldiers were wounded sounds just fine to me. (Correcting your typo of halve.)

The first sentence appears to be missing something:
The theater is [already] packed with a great number of people, [with] a few dozen still pushing in.
The theater is [already] packed with a great number of people, [and] a few dozen [are] still pushing in.

Alternatively a few dozen still pushing in could be considered an absolute phrase, but it doesn't work well in the original sentence. I think it is because the word people is omitted in the absolute. Since people is implied in the absolute, it works better if you reorder the elements of the sentence to recast people as the subject of the main clause, as well as the understood element in the noun of the absolute phrase:
A great number of people are packing the theater, a few dozen still pushing in.

Thanks, Glenn, for giving some specifics.   But you still did not speak to my example of, "dozens are still pushing in."   I'm almost sure the "s" added to dozen is correct, yet it is not talking about specific sets of people.   Am I wrong?

It seems to me that sometimes the 's' is added to 'dozen' for emphasis--not unlike the Hebrew elohiym meaning 'one God' rather than 'many gods'.